The present invention relates to a method and an apparatus for online detection of safe operation and advance detection of unsafe operation of a system or process in the presence of noise in sensor measurements and/or fluctuations in variables measured. More particularly, the present invention provides a method and an apparatus capable of providing advance warnings of a system or process becoming unsafe during operation. Still more particularly, the present invention relates to a method and an apparatus that uses complex/noisy sensor measurements made available from sensors which monitor temperature, viscosity, thermal conductivity, chemical species concentrations, pressure or flow signals as a time-series from a batch, continuous stirred tank, fixed-bed, biochemical, polymerization, fluidized-bed, catalytic/noncatalytic reactors, multiphase, flow or other physical systems operating under varied conditions for advance online identification of normal/safe operation along with detection of abnormal/unsafe operation.
Detection and advance warning of unsafe operation of a system in presence of commonly encountered measurement noise causing fluctuations in monitored sensor signals of either temperature, viscosity, thermal conductivity, mass diffusivity, chemical species concentrations, pressure or flow as time-series from batch, continuous stirred tank, fixed-bed, biochemical, polymerization, fluidized-bed, catalytic/noncatalytic reactors, multiphase, flow or other physical systems is of great importance in process applications. Online identification of normal safe process operation and detection of abnormal unsafe process operation in the presence of measurement noise from monitored digital sequences monitored from sensor apparatus as a time-series still evades satisfactory solution, despite efforts made over the years. The problem is particularly important in the context of chemical reactors where small changes in operating conditions can lead to unsafe process operating conditions resulting in risk to personnel safety, infrastructure, environment and process economics. It is important, therefore, to detect in advance the conditions when the system is initiated into an unsafe operating mode by an automated online procedure that uses time-series measurements that monitor process variable behavior. It is also important that this identification of safe process operation and advance detection of unsafe process operation be obtained when the fluctuations in the monitored signals arise due to process complexities on real time basis so that corrective actions can be taken to avoid the loss to life, property, environment, economics well in advance.
Unsafe process operating conditions in reactors arise when a small change in an operating variable like feed or coolant temperature, flow rate, concentrations of species, viscosity, thermal conductivity, mass diffusivity bring about a drastic change in variable values whereby the system becomes uncontrollable. For example, in the case of temperature, a small increase can induce a large increase in the reaction rates due to the exponential dependency of rate constants on temperature. The increased reaction rates further increases the temperature and this results in the process having the rate of heat generation far exceeding the rate of heat removal by the cooling equipment. Unsafe process operating conditions can damage the reactor vessel, can cause personnel risks, catalyst deactivation, choking, hotspot formation, environmental degradation, economic loss and it is important to a priori detect in advance the conditions which lead to this undesirable behavior so that they may be avoided. Studies related to the safety of process operation may be generally classified in two categories, viz., offline and online.
Offline methods analyze mathematical models of the reactor behavior for specifically chosen reaction systems with the aim of demarcating safe and unsafe regions of operation with respect to the values of the reactor control parameters (Van Welsenaere, R. J. and Froment, G. F., xe2x80x9cParametric Sensitivity and Runaway in Fixed-bed Catalytic Reactorsxe2x80x9d, Vol. 25 Chem. Engg. Sci. 1503 [1970]; Rajadhyaksha, R. A., Vasudeva, K. and Doraiswamy, L. K., xe2x80x9cParametric Sensitivity in Fixed-bed Reactorsxe2x80x9d, Vol. 30 Chem. Engg. Sci. 1399 [1975]; Morbidelli, M. and Varma, A., xe2x80x9cParametric Sensitivity and Runaway in Fixed-bed Catalytic Reactorsxe2x80x9d, Vol. 41 No. 4 Chem. Engg. Sci. 1063 [1986]; Balakotaiah, V., Kodra, D. and Nguyen, D., xe2x80x9cRunaway Limits for Homogeneous and Catalytic Reactorsxe2x80x9d, Vol. 50 No. 7 Chem. Engg. Sci. 1149 [1995]; Heiszwolf, J. J., xe2x80x9cThermal Stability of Reacting Systems in Batch and Continuous Stirred Tank Reactorsxe2x80x9d, Ph. D. Thesis, University of Amsterdam [1998]). Generally, offline methods study the steady-state behavior and not the dynamic behavior to predict safe conditions for process operation. The safe and unsafe regions in relevant process parameters are marked on ready-made charts and tables for look-up. Because the mathematical model of the system is used in offline methods the criteria that are developed to test the safety have a serious drawback in the sense that they are conservative and do not apply in a generalized fashion. This is especially true for complex systems which are commonly encountered in many chemical, catalytic, polymerization, combustion, cracking, multiphase, flow and other physical systems.
On the other hand, few attempts have been made in developing online criteria using time-series signals from processes for the identification of safe operation and detection of unsafe operating conditions (Hub, L. and Jones, J. D., xe2x80x9cEarly Online Detection of Exothermic Reactionsxe2x80x9d, Vol. 5 Plant/Oper. Prog. 221 [1986]). Thus for instance, for exothermic reactions taking place in a reactor, temperature measurements by thermocouples, thermometers, thermistors, are usually available as monitored data of the temperature variable in time. The first derivative and higher-order derivatives of this monitored process variable turning positive are a signature of unsafe operation. But, a very significant drawback of these methods is that computation of derivatives is error-prone because of the commonly encountered fluctuating nature of the measurements especially when the measurement is noisy or the process is associated with fast time scales. Thus, the frequency of monitoring and the sample size used for calculation can have significant bearing on detecting unsafe conditions (Iserman, R., xe2x80x9cProcess Fault Detection Based on Modeling and Estimation Methodsxe2x80x94A Surveyxe2x80x9d, Vol. 20 Automatica 387 [1984]). A possible way is to calculate derivatives by processing the signal with filters. Linear filters when applied to signals obtained from processes following nonlinear mechanisms is again error-prone because the true signal content may be inadvertently filtered. In principle, however, online methodologies have the advantage that they have generalization capability because the methods are applicable even when the mechanistic nature of the process or its mathematical model is unknown. Developing rigorous online methods when adequate modeling information is not known, but, takes into consideration the nonlinear properties of the process implicitly embedded in the data is important. Moreover, these methods would be most useful if they can also handle the presence of measurement noise while analyzing for safety. The advantages of developing online methods and apparatus for these aims would identify conditions when unsafe operation alarms are triggered so that other corrective measures are implemented on the process. On the other hand, as much as detection of unsafe conditions is important, the reverse situation of false alarms being raised is also deleterious to process operation and must be avoided as it affects process economics due to unnecessary shutdowns. Robustness in the method and apparatus for detection of unsafe operation would also imply realizing this objective.
A number of methods, have been studied, in the context of time-series analysis to effectively reduce the noise component in the data arising due to sensor measurement errors or due to fluctuating nature of the process variables. The methods obtain noise reduction by smoothening structures present in the data by FIR and IIR filters based on fast Fourier transform, kernel, and spline estimators (King, R. and Gilles, E. D., xe2x80x9cMultiple Filter Methods for Detection of Hazardous States in an Industrial Plantxe2x80x9d, Vol. 36 AlChE Journal 1697 [1990]; Abarbanel, H. D. I., xe2x80x9cThe Observance of Chaotic Data in Physical Systemsxe2x80x9d; Vol. 65 Rev. Mod. Phys. 1340 [1993]; Cohen, L., xe2x80x9cTime-Frequency Analysisxe2x80x9d, Prentice Hall, New Jersey [1995]; Kantz, H. and Schreiber, T., xe2x80x9cNonlinear Time Series Analysisxe2x80x9d, Cambridge University Press [1997]). However, these methods assume that the noise is dominant in higher frequencies. This assumption is crude and inaccurate for large classes of complex signals. Singular value decomposition techniques and other methods that construct local linear maps, to take care of the nonlinearity have also been developed (Broomhead, D. S. and King, G. P., xe2x80x9cExtracting Qualitative Data from Experimental Dataxe2x80x9d, Vol. 20 Physica D 217 [1986]; Albano, A. M., Muench, J., Schwartz, C., Mees, A. I. and Rapp, P. E., xe2x80x9cSingular Value Decomposition and Grassberger-Procaccia Algorithmxe2x80x9d, Vol. 38 Phys. Rev. A 3017 [1988]). These methods attempt to reconstruct the phase-space and project the original time-series on a subspace spanning the largest fraction of the total variance in the data. However, the method is difficult to apply in a straightforward fashion because of the complex and intricate choices that have to be made and understood for implementation.
Recently, Zaldivar et al U.S. Pat. No 6,195,010 [2001] and Strozzi, F., Zaldivar, J. M., Kronberg, A. E. and Westerterp, K. R., xe2x80x9cOn-line Runaway Detection in Batch Reactors Using Chaos Theory Techniquesxe2x80x9d, Vol. 45 No. 11 AIChE Journal 2429 [1999] have addressed the problem of detecting unsafe operating conditions online by taking into account the intrinsic nonlinearity of the process by estimating divergences of monitored temperature profiles using nonlinear techniques of analysis borrowed from chaos theory. The method is rigorous because it involves phase-space reconstruction using the time-series data by time-delay embedding. The application of this technique, however, involves a-priori knowledge of the time-delay and the embedding dimension as parameters. These parameters when inappropriately selected can lead to wrong estimates of the divergences. Another drawback of this methodology is that the reconstruction of the phase-space and estimation of the divergences is not robust when noise is present in the monitored signals (Strozzi et al, [1999]). It is, therefore, necessary to develop alternate methods that can identify safe process operation and detect unsafe operating conditions when both nonlinearity and noise are present in the measured signals.
Yet another method that has been developed recently, for noise reduction from nonlinear time series data employs wavelet transform which is a generalization of the Fourier transform. The wavelet transform has the advantage of removing the major drawback of Fourier transform, namely, non-resolution of local information in time. Thus when a distinct catastrophic event occurs in a process, Fourier transform analysis in the frequency domain cannot detect the occurrence of this event. Wavelet transforms, on the other hand, can capture the occurrence of the catastrophic event by combining the frequency analysis properties of Fourier transform with inferences possible due to the time localization property of the wavelet transform. It may be appreciated that catastrophic events like onset of unsafe process operation is localized in time and it would be advantageous to use wavelet transform methodologies to detect the occurrence of this condition provided an efficient method is used simultaneously for noise reduction. Hitherto, the Inventors bring out a new method using wavelet transforms, which in an automated way detects in advance unsafe process operation by simultaneously reducing the noise component in the data.
Wavelet transforms have been employed in studying nonlinear, multiscale and nonstationary processes in various interdisciplinary fields (Vetterli, M. and Kovacevic, J., xe2x80x9cWavelets and Subband Codingxe2x80x9d, Prentice Hall, New Jersey [1995]). General methodologies for multiresolution signal processing and multigrid techniques have led to applications in spectroscopy, quantum mechanics, turbulent flows, data compression, image and speech processing (Percival, D. B. and Walden, A. T., xe2x80x9cWavelet Methods for Time Series Analysisxe2x80x9d, Cambridge University Press [2000]). Wavelet transform methods have therefore been increasingly used as tools for studying multiscale, nonstationary and nonlinear processes in various fields. Wavelets are derived from rapidly oscillating functions with mean zero and obtained by scaling of analyzing function to match the desired frequencies with simultaneous translations in time. A wide variety of analyzing functions amenable for discrete and continuous time analysis is known (Strang, G. and Nguyen, T., xe2x80x9cWavelets and Filter Banksxe2x80x9d, Cambridge Press, Wellesley [1996]; Holschneider, M., xe2x80x9cWavelets and Analysis Toolxe2x80x9d, Clarendon Press, Oxford [1995]). Typical wavelet examples are discrete Haar, Daubechies, spanning a wide range of discrete and continuous properties including compact support, bi-orthogonal, spline, Battle-Lemarie, etc. Concisely stated wavelet transforms takes the inner product of a set of above basis wavelets with the available process data xcex8. Repeated applications for various scales a of the basis wavelet function for translations in time b yields scale (i.e., related to frequency) and time inferences to be made from the scalogram (a matrix W of wavelet coefficients w). Analysis of coefficients in the matrix W can be used make conclusions about the time-scale behavior of the process. Alternatively, changing the values of W in a rational way can bring out the true process properties in time and can lead to accurate inferences been drawn regarding the safety aspects of process operation.
In particular, wavelet transforms have been used to create methodologies in reducing noise from signals monitored from a process. The wavelet transform methods for detection of signals in composite signals containing noise are mainly based on the concept of thresholding the wavelet coefficients obtained by a single transformation. Thus, the application of wavelet transform in reducing speckle noise has been described in U.S. Pat. No. 5,497,777 [1996] and in a continuing U.S. Pat. No. 5,619,998 [1997] where a coherent imaging system signal is reduced of speckle noise by nonlinear adaptive thresholding of wavelet coefficients. The resulting image was seen to have an improved signal to noise ratio. The method is independently applied to wavelet scales obtained by a single wavelet transform on a data in a subinterval. However, it would be beneficial to have a process by means of which noise at each scale is considered on a relative basis.
Yet another method for using wavelet transform hard thresholds by setting to zero all wavelet coefficients below a certain threshold at all scales for denoising. In contrast, soft thresholding methods reduce all coefficients at various scales by a threshold value. In both cases the threshold value is determined by statistical calculations and is dependent on the standard deviation of noise and the number of data points. The specified threshold value may be used to evaluate entropy properties and other cost functions to generate a basis that can be used to validate the results of noise reduction. However, the method is dependent on a priori knowledge of the characteristics of the standard deviation of noise in the signal and therefore its applicability to short data length. This is not easily applicable when the signal is nonstationary and the properties of the noise vary. Therefore, considerable improvements in the methods are still needed for accuracy when applying these wavelet transform methods in many precision applications like chemical process plants, complex fluid dynamical flows, medical diagnostics, image analysis, etc. The central problem here is that noise can be present in all frequencies and eliminating components based on statistical thresholding is not sufficient. To find alternatives that address and alleviate these difficulties, new methods utilizing wavelet transform in alternate settings, for denoising process data need to be developed.
Newer methods for the identification and/or separation of composite signals into its deterministic and noisy components without the need for threshold values to be calculated and whose basis has a principled scientific rationale have been recently made. Recognizing that noise can be present at all scales, the principle used for separation between deterministic signal components and noise in a composite signal is that the relative power distribution (RPD) will remain constant for noise at different scales, while that, for the deterministic component RPD will vary, (U.S. Pat. No. 6,208,951 [2001]). Different ways of achieving this separation of noise from the deterministic component is possible. One way is to employ recursive wavelet transforms on a composite signal till the RPD at different scales show constancy. Recursively transformed scales contain information about the local noise content in the original composite signal. Separation of the deterministic components from the noisy signal is therefore possible. Yet another method of separating the deterministic and noise components would be to differentiate the data and carry out the process of wavelet transform on the differentiated data (Roy, M., Ravi Kumar, V., Kulkarni, B. D., Sanderson, J., Rhodes, M. and vander Stappen, M., xe2x80x9cSimple Denoising Algorithm Using Wavelet Transformxe2x80x9d, Vol. 45 No. 11 AIChE Journal 2461 [1999]). Upon differentiation the contributions due to noise moves towards the finer wavelet scales because the process of differentiation converts the uncorrected stochastic process to a first-order moving average process and thereby distributes more of its energy in the finer wavelet scales (i.e., in the high frequency wavelet scales expressed in dyadic format). Therefore, the properties of noise with respect to differentiation can be fruitfully utilized by eliminating those scales contributing to the noise before carrying out inverse wavelet transform. It should be stated that the effectiveness of separation depends on the chosen wavelet basis function. In view of the fact that orthogonal bases yield loss-less wavelet transform of data, its choice would be preferred. It is to be brought out that the methods discussed above do not involve the direct consideration of the properties of noise in the composite signal (composed of true deterministic signal and noise). Placing the noise component in wavelet scales distinct from those of the deterministic component brings about the noise reduction.
Thus, online identification of normal safe process operation and detection of abnormal unsafe process operation in the presence of measurement noise from monitored digital sequences monitored from sensor apparatus as a time-series still evades satisfactory solution, despite efforts made over the years.
Accordingly the present invention has provided a method and an apparatus for online identification of safe operation and advance detection of unsafe operation of a system or a process which is useful and advantageous method and can be applied in a systematic and rational manner using wavelet transforms for denoising with online criteria related to safe process operation. Particularly, the present invention discloses a systematic and improved method for identification of safe process operation and advance detection of unsafe process operation, even when the monitored signals of process variables from the process are noisy, and which allows for inferring effects of changes in process states and operating conditions to be reliably inferred from the monitored process data. The method is robust and is based on scientific rationale and can be used for signals obtained online by sensors monitoring the changes in the process variable(s) as measurements and suitably digitized to rescaled time-series data by analog to digital (A/D) apparatus. Inferences regarding safety in process operation can be made accurately and quickly and is applicable to situations independent of the phenomenological description of the process, of the availability of mathematical models and does not use per-se the operating process parameter values in making the inferences about safe and unsafe process operation.
The main object of the present invention is to provide an improved method for the online identification of safe operation and advance detection of unsafe operation of a system or process.
Another object of the invention is to show that the identification of safe operation and detection of unsafe operating condition can be incorporated effectively in an apparatus monitoring process signals.
Yet another object of the invention is to show that the identification of safe operation and detection of unsafe operating condition can be made in real-time by incorporating the modifications to the monitoring apparatus.
Still another object of the present invention is to provide an apparatus for online identification of safe operation and advance detection of unsafe operation of a system or process that can lead to better and accurate inferences about process behavior.
One more object of the present invention is to bring out that a combination of the above objects in a systematic manner provides a new general framework for the online identification of safe operation and advance detection of unsafe operation of systems or processes.